A simulation model of the three-dimensional architecture of the maize root system

In order to study the nutrient and water uptake of rootsin situ, we need a quantitative three-dimensional dynamic model of the root system architecture. The present model takes into account current observations on the morphogenesis of the maize root system. It describes the root system as a set of root axes, characterised by their orders and their inter-node of origin. The evolution of the simulated pattern is achieved by three processes, occuring at each time step: emission of new primary root axes from the shoot, growth and branching of existing root axes. The elongation of an axis depends on its order, inter-node and local growing conditions. Branches appear acropetally at a specified distance from the apex and from former branches, along ranks facing xylem poles, with a branching angle specific to their order and inter-node. From the three-dimensional branched patterns simulated by the model, various outputs, such as root profiles or cross-section maps can be computed, compared to observed data and used as inputs in uptake models. A number of examples of such possible outputs are presented.     

Fusion of radiostereometric analysis data into computed tomography space: application to the elbow joint

Improvement of joint prostheses is dependent upon information concerning the biomechanical properties of the joint. Radiostereometric analysis (RSA) and electromagnetic techniques have been applied in previous cadaver and in vivo studies on the elbow joint to provide valuable information concerning joint motion axes. However, such information is limited to mathematically calculated positions of the axes according to an orthogonal coordinate system and is difficult to relate to individual skeletal anatomy. The aim of this study was to evaluate the in vivo application of a new fusion method to provide three-dimensional (3D) visualization of flexion axes according to bony landmarks. In vivo RSA data of the elbow joint's flexion axes was combined with data obtained by 3D computed tomography (CT). Results were obtained from five healthy subjects after one was excluded due to an instable RSA marker. The median error between imported and transformed RSA marker coordinates and those obtained in the CT volume was 0.22 mm. Median maximal rotation error after transformation of the rigid RSA body to the CT volume was 0.003 degrees . Points of interception with a plane calculated in the RSA orthogonal coordinate system were imported into the CT volume, facilitating the 3D visualization of the flexion axes. This study demonstrates a successful fusion of RSA and CT data, without significant loss of RSA accuracy. The method could be used for relating individual motion axes to a 3D representation of relevant joint anatomy, thus providing important information for clinical applications such as the development of joint prostheses.     

A method for planar biaxial mechanical testing that includes in-plane shear.

A limitation in virtually all planar biaxial studies of soft tissues has been the inability to include the effects of in-plane shear. This is due to the inability of current mechanical testing devices to induce a state of in-plane shear, due to the added cost and complexity. In the current study, a straightforward method is presented for planar biaxial testing that induces a combined state of in-plane shear and normal strains. The method relies on rotation of the test specimen's material axes with respect to the device axes and on rotating carriages to allow the specimen to undergo in-plane shear freely. To demonstrate the method, five glutaraldehyde treated bovine pericardium specimens were prepared with their preferred fiber directions (defining the material axes) oriented at 45 deg to the device axes to induce a maximum shear state. The test protocol included a wide range of biaxial strain states, and the resulting biaxial data re-expressed in material axes coordinate system. The resulting biaxial data was then fit to the following strain energy function W: [equation: see text] where E'ij is the Green's strain tensor in the material axes coordinate system and c and Ai are constants. While W was able to fit the data very well, the constants A5 and A6 were found not to contribute significantly to the fit and were considered unnecessary to model the shear strain response. In conclusion, while not able to control the amount of shear strain independently or induce a state of pure shear, the method presented readily produces a state of simultaneous in-plane shear and normal strains. Further, the method is very general and can be applied to any anisotropic planar tissue that has identifiable material axes.     

In vitro assessment of a motion-based optimization method for locating the talocrural and subtalar joint axes

The locations of the joint axes of the ankle complex vary considerably between subjects, yet no noninvasive method with demonstrated accuracy exists for locating these axes. The moments of muscle and ground reaction forces about the joint axes are dependent on axis locations, making knowledge of these locations critical to accurate musculoskeletal modeling of the foot and ankle. The accuracy of a computational optimization method that fits a two-revolute model to measured motion was assessed using computer-generated data, a two-revolute mechanical linkage, and three lower-leg cadaver specimens. Motions were applied to cadaver specimens under axial load while bone-mounted markers attached to the tibia, talus, and calcaneus were tracked using a video-based motion analysis system. Estimates of the talocrural and subtalar axis locations were computed from motions of the calcaneus relative to the tibia using the optimization method. These axes were compared to mean helical axes computed directly from tibia, talus, and calcaneus motions. The optimization method performed well when the motions were computer-generated or measured in the mechanical linkage, with angular differences between optimization and mean helical axes ranging from 1 deg to 5 deg. In the cadaver specimens, however, these differences exceeded 20 deg. Optimization methods that locate the anatomical joint axes of the ankle complex by fitting two revolute joints to measured tibia-calcaneus motions may be limited because of problems arising from non-revolute behavior.     

Optimum-transformation of plant species cover-abundance values

Most of the methods used in the multivariate analysis of data on vegetation and environment, or transformations implied in such methods, put disproportionate emphasis on species with a relatively wide ecological amplitude occurring with relatively high cover-abundance values, and/or rare species. This problem can be overcome to some extent by reducing the cover-abundance values to presence-absence data, but this means a severe loss of information. A standardization of values by species maxima as is done automatically in some programs, may lead to an undesirable emphasis on species represented with low values only.In this paper a method is presented, by which relatively low cover-abundance values of species are upweighted to an arbitrarily chosen higher value, if these low values are considered to indicate an optimum response of that particular species. The method has been tested on a selection of 40 phytosociological relevés from dune slacks in the Voorne dunes, as well as on the Dune Meadow data set used in the textbook of Jongman et al. (1987). The cluster structure obtained with the optimum-transformation appears to be clearer and the contribution of typical dune slack species to the cluster structure increased significantly. Canonical correspondence analysis of the transformed data gave slightly more important main axes.Abbreviations CA = Correspondence Analysis - CCA = Canonical Correspondence Analysis - DOL = Detection of Optimality Level - SWOM = Standardized Weighted Optimality Measure - WPGMA = Weighted Pair Group Method Average linking clustering     

Gait and posture discrimination in sheep using a tri-axial accelerometer

Temporo-spatial observation of the leg could provide important information about the general condition of an animal, especially for those such as sheep and other free-ranging farm animals that can be difficult to access. Tri-axial accelerometers are capable of collecting vast amounts of data for locomotion and posture observations; however, interpretation and optimization of these data records remain a challenge. The aim of the present study was to introduce an optimized method for gait (walking, trotting and galloping) and posture (standing and lying) discrimination, using the acceleration values recorded by a tri-axial accelerometer mounted on the hind leg of sheep. The acceleration values recorded on the vertical and horizontal axes, as well as the total acceleration values were categorized. The relative frequencies of the acceleration categories (RFACs) were calculated in 3-s epochs. Reliable RFACs for gait and posture discrimination were identified with discriminant function and canonical analyses. Post hoc predictions for the two axes and total acceleration were conducted, using classification functions and classification scores for each epoch. Mahalanobis distances were used to determine the level of accuracy of the method. The highest discriminatory power for gait discrimination yielded four RFACs on the vertical axis, and five RFACs each on the horizontal axis and total acceleration vector. Classification functions showed the highest accuracy for walking and galloping. The highest total accuracy on the vertical and horizontal axes were 90% and 91%, respectively. Regarding posture discrimination, the vertical axis exhibited the highest discriminatory power, with values of RFAC (0, 1]=99.95% for standing; and RFAC (−1, 0]=99.50% for lying. The horizontal axis showed strong discrimination for the lying side of the animal, as values were in the acceleration category of (0, 1] for lying on the left side and (−1, 0] on the right side. The algorithm developed by the method employed in the present study facilitates differentiation of the various types of gait and posture in animals from fewer data records, and produces the most reliable acceleration values from only one axis within a short time frame. The present study introduces an optimized method by which the tri-axial accelerometer can be used in gait and posture discrimination in sheep as an animal model.     

Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis

Indirect gradient analysis, or ordination, is primarily a method of exploratory data analysis. However, to support biological interpretations of resulting axes as vegetation gradients, or later confirmatory analyses and statistical tests, these axes need to be stable or at least robust into minor sampling effects. We develop a computer-intensive bootstrap (resampling) approach to estimate sampling effects on solutions from nonlinear ordination.We apply this approach to simulated data and to three forest data sets from North Carolina, USA and examine the resulting patterns of local and global instability in detrended correspondence analysis (DCA) solutions. We propose a bootstrap coefficient, scaled rank variance (SRV), to estimate remaining instability in species ranks after rotating axes to a common global orientation. In analysis of simulated data, bootstrap SRV was generally consistent with an equivalent estimate from repeated sampling. In an example using field data SRV, bootstrapped DCA showed good recovery of the order of common species along the first two axes, but poor recovery of later axes. We also suggest some criteria to use with the SRV to decide how many axes to retain and attempt to interpret.Abbreviations DCA= detrended correspondence analysis - SRV= scaled rank variance     

Calculating the axes of rotation for the subtalar and talocrural joints using 3D bone reconstructions

Orientation of the subtalar joint axis dictates inversion and eversion movements of the foot and has been the focus of evolutionary and clinical studies for a number of years. Previous studies have measured the subtalar joint axis against the axis of the whole foot, the talocrural joint axis and, recently, the principal axes of the talus. The present study introduces a new method for estimating average joint axes from 3D reconstructions of bones and applies the method to the talus to calculate the subtalar and talocrural joint axes. The study also assesses the validity of the principal axes as a reference coordinate system against which to measure the subtalar joint axis. In order to define the angle of the subtalar joint axis relative to that of another axis in the talus, we suggest measuring the subtalar joint axis against the talocrural joint axis. We present corresponding 3D vector angles calculated from a modern human skeletal sample. This method is applicable to virtual 3D models acquired through surface-scanning of disarticulated 'dry' osteological samples, as well as to 3D models created from CT or MRI scans.     

Physical Models for Exploring DNA Topology

Abstract

Two types of physical models have been developed for treating DNA molecules whose topology is of interest The two model motifs combine jacks-and-straws molecular representations with flexible tubing in different proportions. Both motifs present a low-resolution construct of DNA that retains helix axes, strand individuality and the distinguishabiity of the major and minor grooves. Molecules whose double helix axes are branched are modelled by stiff double helices and flexible branch sites. Supercoiled and knotted DNA molecules are modelled on a smaller scale, in a system in which a flexible backbone is supported by a series of stiff helical struts; removal of this scaffolding immediately reveals the linking of the strands. The models are light and easy to construct. They may be used either for demonstrations or as a research tool that assists the interpretation data.     

Discovering biogeographic and ecological clusters with a graph theoretic spin on factor analysis

Factor analysis (FA) has the advantage of highlighting each semi‐distinct cluster of samples in a data set with one axis at a time, as opposed to simply arranging samples across axes to represent gradients. However, in the case of presence–absence data it is confounded by absences when gradients are long. No statistical model can cope with this problem because the raw data simply do not present underlying information about the length of such gradients. Here I propose an easy way to tease out this information. It is a simple emendation of FA called stepping down, which involves giving an absence a negative value when the missing species nowhere co‐occurs with the species found in the relevant sample. Specifically, a binary co‐occurrence graph is created, and the magnitude of negative values is made a function of how far the graph must be traversed in order to link the missing species with each species that is present. Simulations show that standard FA yields inferior results to FA based on stepped‐down matrices in terms of mapping clusters into axes one‐by‐one. Standard FA is also uninformative when applied to a global bat inventory data set. Step‐down FA (SDFA) easily flags the main biogeographic groupings. Methods like correspondence analysis, non‐metric multidimensional scaling, and Bayesian latent variable modelling are not commensurate with SDFA because they do not seek to find a one‐to‐one mapping of axes and clusters. Stepping down seems promising as a means of illustrating clusters of samples, especially when there are subtle or complex discontinuities in gradients.     

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three "non-orthogonal effective axes" that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90 degrees was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.     

On intrinsic equivalences of the finite helical axis,the instantaneous helical axis,and the SARA approach. A mathematical perspective

Accurate determination of joint axes is essential for understanding musculoskeletal function. Whilst numerous algorithms to compute such axes exist, the conditions under which each of the methods performs best remain largely unknown. Typically, algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance. We derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data: finite helical axes (FHA), instantaneous helical axes (IHA) and SARA (symmetrical axis of rotation approach), including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes. Through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the FHA and SARA approach are equivalent for the analysis of two time frames. Moreover, we show that the position of a helical axis derived from the IHA using positional data is affected by a systematic error perpendicular to the true axis direction, whereas the axis direction is identical to those computed with either the FHA or SARA approach (true direction). Finally, with an appropriate choice of weighting factors the mean FHA (MFHA) method is equivalent to the Symmetrical Centre of Rotation Estimation (SCoRE) algorithm for determination of a Centre of Rotation (CoR), and similarly, equivalent to the SARA algorithm for determination of an Axis of Rotation (AoR). The deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient, robust methods for determining AoRs and CoRs with confidence.     

Finding a common ordination for several data sets by individual differences scaling

Individual differences scaling is a multidimensional scaling method for finding a common ordination for several data sets. An individual ordination for each data set can then be derived from the common ordination by adjusting the axis lengths so as to maximize the correlations between observed proximities and individual ordination distances. The importance of the various axes for each data set and the mutual similarities and goodness of fit for the individual data sets are described by weight plots. As an example, 46 soft-water lakes in eastern Finland are ordinated on two dimensions according to 3 chemical data sets (water in summer and autumn, sediment) and 4 biological sets (major phytoplankton groups, phytoplankton, surface sediment diatom and cladoceran assemblages). The method seems to be effective as a means of ordination for obtaining the common ordination for the data sets. The major taxonomic groups gave the ordination which differed most clearly from the ordinations of the other data sets. Phytoplankton was most poorly ordinated in all the analyses. The other data sets were fairly coherent. When only biological data sets were ordinated, the diatoms and cladocerans showed rather different patterns. It seems that the cladocerans are best correlated with water chemistry, both according to weights in the joint analysis, and according to correlation between the axes from the biological data sets and the chemical variables.Abbreviations CCA = Canonical correspondence analysis - IDS = Individual differences scaling - MDS = multidimensional scaling - PCA = Principal components analysis     

A procedure for determining angular positional data relative to the principal axes of the human body

This paper describes a simple computational procedure for determining angular displacement-time histories of human motion from three-dimensional cine data. The method is based on algebraic transformations of coordinates and coordinate axes. Through these coordinate transformations data was acquired for a multi-axial tumbling skill to illustrate angular displacement-time data relative to the moving coordinate system described by the human body through space.     

Computed tomography analysis of radiostereometric data to determine flexion axes after total joint replacement: Application to the elbow joint

Kinematic analysis for in vivo assessment of elbow endoprostheses requires knowledge of the exact positions of motion axes relative to bony landmarks or the prosthesis. A prosthesis-based reference system is required for comparison between individuals and studies. The primary aim of this study was to further develop an earlier described algorithm for fusion of radiostereometric analysis (RSA) data and data obtained in 3D computed tomography (CT) for application to the elbow after total joint replacement. The secondary aim was to propose a method for marking of prostheses in 3D CT, enabling definition of a prosthesis-based reference system. Six patients with elbow endoprostheses were investigated.The fusion of data made it possible to visualize the motion axes in relation to the prostheses in the 3D CT volume. The differences between two repeated positioning repetitions of the longitudinal prosthesis axis were less than 0.6° in the frontal and sagittal planes. Corresponding values for the transverse axis were less than 0.6° in the frontal and less than 1.4° (in four out of six less than 0.6°) in the horizontal plane.This study shows that by fusion of CT and RSA data it is possible to determine the accurate position of the flexion axes of the elbow joint after total joint replacement in vivo. The proposed method for implant marking and registration of reference axes enables comparison of prosthesis function between patients and studies.     

Double calibration: an accurate, reliable and easy-to-use method for 3D scapular motion analysis

The most recent non-invasive methods for the recording of scapular motion are based on an acromion marker (AM) set and a single calibration (SC) of the scapula in a resting position. However, this method fails to accurately measure scapular kinematics above 90° of arm elevation, due to soft tissue artifacts of the skin and muscles covering the acromion. The aim of this study was to evaluate the accuracy, and inter-trial and inter-session repeatability of a double calibration method (DC) in comparison with SC. The SC and DC data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation (0-180°). They were compared with palpation of the scapula using a scapula locator. DC data was not significantly different from palpation for 5/6 axes of rotation tested (Y, X, and Z in abduction and flexion), where as SC showed significant differences for 5/6 axes. The root mean square errors ranged from 2.96° to 4.48° for DC and from 6° to 9.19° for SC. The inter-trial repeatability was good to excellent for SC and DC. The inter-session repeatability was moderate to excellent for SC and moderate to good for DC. Coupling AM and DC is an easy-to-use method, which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion. It can be applied to the measurement of shoulder motion in many fields (sports, orthopaedics, and rehabilitation), especially when large ranges of arm motion are required.     

A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.     

Automated segmentation of molecular subunits in electron cryomicroscopy density maps

Electron cryomicroscopy (cryoEM) is capable of imaging large macromolecular machines composed of multiple components. However, it is currently only possible to achieve moderate resolution at which it may be possible to computationally extract the individual components in the machine. In this work, we present application details of an automated method for detecting and segmenting the components of a large machine in an experimentally determined density map. This method is applicable to object with and without symmetry and takes advantage of global and local symmetry axes if present. We have applied this segmentation algorithm to several cryoEM data sets already deposited in EMDB with various complexities, symmetries and resolutions and validated the results using manually segmented density and available structures of the components in the PDB. As such, automated segmentation could become a useful tool for the analysis of the ever-increasing number of structures of macromolecular machines derived from cryoEM.     

Expression of joint moment in the joint coordinate system

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as "motor torque." However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N?m to 22.3 N?m between both projections at the shoulder, while differences ranged from 0.8 N?m to 3.0 N?m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.